Bosco

In order not to have two yellows next to each other,  

the three yellows must occupy squares 1, 3, and 5. 

That leaves squares 2 and 4 to fill, and two colors  

to do it with. There are only four ways. 

Blue Blue     Red Red     Blue Red     Red Blue  

So, the answer is four ways.  

_.

     A_{large square}  =  6.25 units²  

     The base of each triangle is 1 unit. 

     There are 2¹/₂ bases going across.  

     So the side of the square is 2¹/₂ units.  

     Two and a half squared is six and a quarter.  

_.

          Area = 144 units²    

          If one of the angles is 90^o   

          then all of the angles are 90^o   

          and this rhombus is a square.  

_.

The coefficient of y⁴ in the expansion will be 81.   

Combine terms of (2y – 5 + y – 6)⁴  to  (3y – 11)⁴   

There will be only one term raised to the fourth power   

and that's the "3y" term ...  3 raised to the fourth is 81.   

_.

A = 100 units²     

Perimeter 40 and diagonal 10 • sqrt(2) indicate that this     

figure is the special case of rectangle, which is a square.    

Each side is 10, therefore the area is 10 • 10 = 100.     

Deleted.  I misread the question.

                 7!             5040  

₇P₇  =  –––––––  =  ––––––  =  5040       

             (7 – 7)!           1   

You might question zero in the denominator,   

but zero factorial is defined as 1 so it's okay.  

_.

               AB + CD  

Area  =  —–—–—–  •  height   

                     2   

That's just the formula for the area of a trapezoid.   

Without specific values, I can't take it any further.  

_.

A_{big square}  =  6.25 units²  

The base of each triangle is 1 unit. 

There are 2¹/₂ bases going across.  

So the side of the square is 2¹/₂ units.  

Two and a half squared is six and a quarter.  

_.